Recall that there are two types of calcium bonds in curd:
1) The bonds between micelles that occur after rennet cleaves the k-casein, and
2) The intra-micellar bonds
When you rennet at a high pH, as happens with asiago, those intra-micellar bonds have not had an opportunity to break very much. Some breakage is necessary, otherwise, you will wind up with a cheese that takes drastically long to age, as tends to happen with, say, true grana types.
If you do not acidify the milk before renetting, you need to acidify the cheese. Acidification does not remove calcium. It can't go anywhere, the whey is already gone, this is a low moisture cheese. But, what can happen is that the bonds will break. They need to break at least to a post-brine pH of 5.2. If they do not, it is not the end of the world, but texture issues may develop, and it will take longer to age.
So no, not highly decalcified cheese. All high calcium means is high rennet pH. Without the intra-micellar degradation, quite a lot of calcium remains. Think about the two types of bonds and how acid affects them.